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Substantive Rationality and Backward Induction

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  • Joseph Y. Halpern

    (Cornell University)

Abstract

Aumann has proved that common knowledge of substantive rationality implies the backwards induction solution in games of perfect information. Stalnaker has proved that it does not. Roughly speaking, a player is substantively rational if, for all vertices $v$, if the player were to reach vertex $v$, then the player would be rational at vertex $v$. It is shown here that the key difference between Aumann and Stalnaker lies in how they interpret this counterfactual. A formal model is presented that lets us capture this difference, in which both Aumann's result and Stalnaker's result are true (under appropriate assumptions).

Suggested Citation

  • Joseph Y. Halpern, 2000. "Substantive Rationality and Backward Induction," Game Theory and Information 0004008, University Library of Munich, Germany.
    • Handle: RePEc:wpa:wuwpga:0004008
    Note: Type of Document - PDF; prepared on Unix; pages: 12; figures: included. To appear, Games and Economic Behavior.
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    File URL: https://econwpa.ub.uni-muenchen.de/econ-wp/game/papers/0004/0004008.pdf
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    References listed on IDEAS

    as
    1. Samet, Dov, 1996. "Hypothetical Knowledge and Games with Perfect Information," Games and Economic Behavior, Elsevier, vol. 17(2), pages 230-251, December.
    2. Binmore, Ken, 1987. "Modeling Rational Players: Part I," Economics and Philosophy, Cambridge University Press, vol. 3(2), pages 179-214, October.
    3. Philip J. Reny, 1992. "Rationality in Extensive-Form Games," Journal of Economic Perspectives, American Economic Association, vol. 6(4), pages 103-118, Fall.
    4. Stalnaker, Robert, 1996. "Knowledge, Belief and Counterfactual Reasoning in Games," Economics and Philosophy, Cambridge University Press, vol. 12(2), pages 133-163, October.
    5. Stalnaker, Robert, 1998. "Belief revision in games: forward and backward induction1," Mathematical Social Sciences, Elsevier, vol. 36(1), pages 31-56, July.
    6. Aumann, Robert J., 1995. "Backward induction and common knowledge of rationality," Games and Economic Behavior, Elsevier, vol. 8(1), pages 6-19.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Giacomo Bonanno, 2022. "Rational Play in Extensive-Form Games," Games, MDPI, vol. 13(6), pages 1-20, October.
    2. Battigalli, Pierpaolo & De Vito, Nicodemo, 2021. "Beliefs, plans, and perceived intentions in dynamic games," Journal of Economic Theory, Elsevier, vol. 195(C).
    3. Tarbush, Bassel, 2016. "Counterfactuals in “agreeing to disagree” type results," Mathematical Social Sciences, Elsevier, vol. 84(C), pages 125-133.
    4. Sandholm, William H. & Izquierdo, Segismundo S. & Izquierdo, Luis R., 2019. "Best experienced payoff dynamics and cooperation in the Centipede game," Theoretical Economics, Econometric Society, vol. 14(4), November.
    5. Bonanno, Giacomo, 2013. "A dynamic epistemic characterization of backward induction without counterfactuals," Games and Economic Behavior, Elsevier, vol. 78(C), pages 31-43.
    6. Bach, Christian W. & Heilmann, Conrad, 2009. "Agent connectedness and backward induction," LSE Research Online Documents on Economics 27000, London School of Economics and Political Science, LSE Library.
    7. Giacomo Bonanno, 2012. "Epistemic foundations of game theory," Working Papers 70, University of California, Davis, Department of Economics.
    8. Giacomo Bonanno, 2011. "Reasoning about strategies and rational play in dynamic games," Working Papers 9, University of California, Davis, Department of Economics.
    9. Bonanno, Giacomo, 2013. "A dynamic epistemic characterization of backward induction without counterfactuals," Games and Economic Behavior, Elsevier, vol. 78(C), pages 31-43.
    10. Bonanno, Giacomo, 2003. "A syntactic characterization of perfect recall in extensive games," Research in Economics, Elsevier, vol. 57(3), pages 201-217, September.
    11. Giacomo Bonanno, 2008. "Non-cooperative game theory," Working Papers 86, University of California, Davis, Department of Economics.
    12. Asheim, Geir B., 2002. "On the epistemic foundation for backward induction," Mathematical Social Sciences, Elsevier, vol. 44(2), pages 121-144, November.
    13. Giacomo Bonanno, 2008. "Non-cooperative game theory," Working Papers 159, University of California, Davis, Department of Economics.
    14. Graciela Kuechle, 2009. "What Happened To The Three‐Legged Centipede Game?," Journal of Economic Surveys, Wiley Blackwell, vol. 23(3), pages 562-585, July.
    15. Giacomo Bonanno, 2011. "Reasoning about strategies and rational play in dynamic games," Working Papers 1111, University of California, Davis, Department of Economics.
    16. Giacomo Bonanno, 2018. "Behavior and deliberation in perfect-information games: Nash equilibrium and backward induction," International Journal of Game Theory, Springer;Game Theory Society, vol. 47(3), pages 1001-1032, September.
    17. Giacomo Bonanno, 2013. "Counterfactuals and the Prisoner?s Dilemma," Working Papers 137, University of California, Davis, Department of Economics.
    18. Giacomo Bonanno, 2021. "Rational play in games: A behavioral approach," Working Papers 344, University of California, Davis, Department of Economics.

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    More about this item

    Keywords

    Substantive rationality; backward induction; games of perfect information; counterfactuals;
    All these keywords.

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • C80 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - General

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